Question: Solve for $x$ and $y$ using elimination. ${6x-2y = 16}$ ${5x-5y = -20}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-2$ ${30x-10y = 80}$ $-10x+10y = 40$ Add the top and bottom equations together. $20x = 120$ $\dfrac{20x}{{20}} = \dfrac{120}{{20}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {6x-2y = 16}\thinspace$ to find $y$ ${6}{(6)}{ - 2y = 16}$ $36-2y = 16$ $36{-36} - 2y = 16{-36}$ $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ You can also plug ${x = 6}$ into $\thinspace {5x-5y = -20}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ - 5y = -20}$ ${y = 10}$